2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163191Given a K3 surface S, we show that the relative intermediate Jacobian of the universal family of Fano 3-folds V containing S as an anticanonical divisor is a Lagrangian fibration. The proof uses variations of the mixed Hodge structure of the pair (V,S).10 pages; final version as published in Math. AnnalenAlgebraic GeometryDynamical Systems14J45,14D07,14H10,14K30,70H06text